Call x the proportion of people in a country who decide to behave in a corrupt and dishonest way. Assume that when people are honest, their payoff is L. Assume that when they behave in a corrupt way and are caught, their payoff is 0, but if they are not caught, their payoff is C > L. Assume that p is the probability of being caught when corrupt and that p is a negative function of x with p(0) = 1 and p(1) = 0. Show that there are two Nash equilibria, one where all people behave in a corrupt way and one where all are honest. Explain why these are Nash equilibria. Is there a third equilibrium? Explain how these equilibria come about.